snub cube

It is important in the study of the snub cube.

For instance, the snub cube is created in two steps.

For a snub cube with unit edge length, use the following coordinates instead:

An alternation of a great rhombicuboctahedron produces a snub cube.

Here t is the tribonacci constant (see snub cube).

For example, the snub cube has a clockwise and counterclockwise form which are identical across mirror images.

Secondly, that polyhedron is alternated into a snub cube.

Fig. 5-34 shows a partial honeycomb of the alternation with only snub cube cells show.

There are also two Archimedean solids with 60 edges: the snub cube and the icosidodecahedron.

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube.

By this definition, even highly-symmetric and enantiomorphic polytopes such as the snub cube are not chiral.

For example, the snub cube:

The icosahedron, snub cube and snub dodecahedron are the only three convex ones.

In geometry, a pentagonal icositetrahedron is a Catalan solid which is the dual of the snub cube.

Depending on which set of vertices are alternated, the resulting snub cube can have a clockwise or counterclockwise twist.

If the original snub cube has edge length 1, its dual pentagonal icositetrahedron has side lengths and .

The snub cube is one of a family of uniform polyhedra related to the cube and regular octahedron.

The only snub polyhedron with the chiral octahedral group of symmetries is the snub cube.

It has 2 snub cubes connected by 12 tetrahedrons, 6 square antiprisms, and 8 octahedrons, with 48 tetrahedrons in the alternated gaps.

In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles.

For a snub cube with edge length 1, its surface area is and its volume is , where t is the tribonacci constant .

Such polyhedra may have various convex hulls, including the truncated cube, the snub cube, or the rhombicuboctahedron, as in the small cubicuboctahedron at right.

It makes snub cubes from the truncated cuboctahedra, square antiprisms from the octagonal prisms and with new tetrahedral cells created in the gaps.

The snub cube has two special orthogonal projections, centered, on two types of faces: triangles, and squares, correspond to the A and B Coxeter planes.

The icosahedron, as a uniform snub tetrahedron, is similar to these snub-pair compounds: compound of two snub cubes and compound of two snub dodecahedra.